Lattice BGK Models For The Convection Diffusion Equation With Source Term

The lattice Boltzmann method is a new numerical technique based on kinetic theory to simulate fluid flows in recent years. Compared with other computational fluid dynamics approaches, the method is simple, intrinsically parallel, and easy to incorporate complex boundary conditions. Although, there has a progress in employing the lattice Boltzmann equation for fluid dynamics and modeling complex physics in fluids recently, there are some problems need to be solved, such as there are different assumptions about source term in the original LBGK models for the convection-diffusion equation with source term.In this paper three improved LBGK models are given. These three models remove all assumptions by rewrite the evolution equation. To test the improved LBGK models proposed in the paper, numerical simulations of diffusion equation with source term, reaction-diffusion equation and convection-diffusion equation with source term are carried out at chapter 3. It is found that the simulation results of improved LBGK models are in excellent agreement with the analytical solutions. It is also shown that the numerical accuracy of the improved LBGK model is much better than that of the existing models. At chapter 4 we use the improved LBGK model I to simulate the CIMA system. The process of Turing patterns forms in two-dimensional space are given.